Are deep learning models suitable for training with sparse data?
The problem isn't the GAN but the implementation of its discriminator which is typically a convolutional neural network (CNN).  CNNs have trouble with sparse data.  They require dense data to learn well.  There are ways to work around this.  See the following for some ideas:


Sparse and Dense Data with CNNs: Depth Completion and Semantic Segmentation
Sparse data in deep learning
SECOND: Sparsely Embedded Convolutional Detection